Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/142925
Periods of Modular GL2-type Abelian Varieties and p-adic Integration
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
Let F be a number field and an integral ideal. Let f be a modular newform over F of level with rational Fourier coefficients. Under certain additional conditions, Guitart and colleagues [Guitart et al. 16[Guitart et al. 16] X. Guitart, M. Masdeu, and M. Haluk Şengün. "Uniformization of Modular Elliptic Curves via p-adic Periods." J. Algebra 445 (2016), 458-502. MR 3418066 [Crossref], [Web of Science ®] , [Google Scholar] ] constructed a p-adic lattice which is conjectured to be the Tate lattice of an elliptic curve Ef whose L-function equals that of f. The aim of this note is to generalize this construction when the Hecke eigenvalues of f generate a number field of degree d ⩾ 1, in which case the geometric object associated with f is expected to be, in general, an abelian variety Af of dimension d. We also provide numerical evidence supporting the conjectural construction in the case of abelian surfaces.
Matèries (anglès)
Citació
Citació
GUITART MORALES, Xavier and MASDEU, Marc. Periods of Modular GL2-type Abelian Varieties and p-adic Integration. Experimental Mathematics. 2017. Vol. 27, num. 3, pags. 344-361. ISSN 1058-6458. [consulted: 14 of August of 2026]. Available at: https://hdl.handle.net/2445/142925